<p>Aneuploidy induces chromosomal scale alterations in gene dosage, impacting organismal proliferation yet serving as a driver for adaptive evolution. The complexity of gene dosage effects makes it challenging to elucidate the causal genetic basis of aneuploid consequence. Here, using loss-of-function screening with Synthetic Chromosome Rearrangement and Modification by LoxP-mediated Evolution (SCRaMbLE) in synthetic aneuploid yeast, in conjunction with gain-of-function testing in euploid yeast, we established a sufficient and necessary framework and discovered cases of nonlinear polygenic dosage effects in driving aneuploid phenotypes. We identified an emergent effect resulting from copy number alterations in a locus of five genes, which enhance trehalose biosynthesis and confer heat tolerance in aneuploid yeast with additional chromosome III. Additionally, a gene dosage-dependent antagonistic epistasis effect of two genes <i>YCL039W</i> and <i>YCL037C</i> determines rapamycin resistance in aneuploid yeast by regulating the Ras signaling pathway. Moreover, several cases of sufficiency-necessity asymmetries were found for other aneuploid traits. Together, our findings provide direct evidence of various dosage-dependent nonlinear polygenic interactions in shaping aneuploid phenotypes and advance understanding of the genetic basis of cellular adaptive evolution.</p>